Friction Force and Decelerating Boat

1. The problem statement, all variables and given/known data
A 1000 kg boat is travelling at 100km/h when its engine is shut off.The magnitude of the frictional force ## \vec f_k## between boat and the water is proportional to the speed v of the boat:##f_k=70v##,where v is in meters per second and ##f_k## is in newtons.Find the time required for the boat to slow to 45 km/h

2. Relevant equations
## \vec F=m \vec a##
##v-v_0=at##

3. The attempt at a solution
I turned km/h to m/s which its ##100km/h=27.7 m/s## and ##45km/h=12.5m/s##
then ;
##ma=-70v##
here the connfusing part is ##a## decreases when v decreases.Theres no constant decelaration.I thought integral but without distance I stucked.
##∫mdv=∫-70vdt##

##ma=-70v##
here the connfusing part is ##a## decreases when v decreases.Theres no constant decelaration.I thought integral but without distance I stucked.

Indeed the deceleration is not constant. Note that ##a = dv/dt## and so what you have is a differential equation describing how velocity changes with time. You will need to solve this differential equation.

Indeed the deceleration is not constant. Note that ##a = dv/dt## and so what you have is a differential equation describing how velocity changes with time. You will need to solve this differential equation.

I didnt learn diff equation.I am fresman student and uni teaches us second year.Like I have no clue

That's not the correct equation. You need to separate the variables.
So you can do integrals and differentials separately, right? I guess your only problem is to set up differential equations using the given data?